Simple Equations(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

SIMPLE EQUATIONS MCQs

Total Questions : 118 | Page 8 of 12 pages

Ethan is given the responsibility of buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog cost twice as much as the supplies for a cat. He needs to feed 164 cats and 24 dogs. His budget is Rs. 4240. How much can Ethan spend on each dog for food and medication? [4 MARKS]

Discuss Question

Answer: Option A. ->
:

Framing the equation 2 Marks
Steps: 1 Mark
Result: 1 Mark
Let the expenditure on a cat be $y$
The expenditure on a dog $= 2 y$ .
Total expenditure on cats $= 164 \times y = 164 y$
Total expenditure of dogs $= 24 \times 2 y = 48 y$
According to question:
$164 y + 24 \times 2 y = 4240$
$\Rightarrow 164 y + 48 y = 4240$
$\Rightarrow 212 y = 4240$
$\Rightarrow y = \frac{4240}{212} = 20$
Hence, expenditure of a dog $= 2 y = 40$
So, for 24 dogs the total expenditure is
$= 24 \times 40 = R s .960$

Question 72.

(a) Aditya has a certain number of pencils. The cost of pencils is 10 greater than 4 times the number of pencils which Aditya has. The total cost of the pencils is Rs 162. Frame the equation and find the number of pencils.
(b) People of Sundargram planted a total of 102 trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees was two more than three times the number of fruit trees. What was the number of fruit trees? [4 MARKS]

Discuss Question

Answer: Option A. ->
:
(a) Steps: 1 Mark
Result: 1 Mark
(b) Steps: 1 Mark
Result: 1 Mark
(a) Let Aditya have x pencils
Now 4 times the number of pencils which Aditya has is

4 \times x = 4 x

10 greater than

4 x = 4 x + 10

Now, given that the total cost is Rs 162, we get

(4 x + 10) = 162

\Rightarrow 4 x = 162 - 10

\Rightarrow 4 x = 152

\Rightarrow x = \frac{152}{4}

\Rightarrow x = 38

So, Aditya has 38 pencils.
(b) Total trees planted = 102
Let the number of fruit trees planted be

x

∴

The number of non-fruit trees planted is

3 x + 2

No. of Non-fruit trees + No. of fruit trees = Total no. of trees

3 x + 2

x

102

4 x + 2 = 102

2 x + 1 = 51

2 x = 50

x = 25

Therefore no. of fruit trees was 25.

Question 73.

After 7 years Sarosh's father's age will be 3 times that of Sarosh's age which will be equal to 6 times of Sarosh's present age. What is the sum of their present ages? [4 MARKS]

Discuss Question

Answer: Option A. ->
:

Framing of equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Let Sarosh's present age be $x$
After 7 years, Sarosh's age will be $x + 7$
Father's age after 7 years is $3 (x + 7)$
This is equal to 6 times Sarosh's present age $= 6 x$
So, $6 x = 3 (x + 7) = 3 x + 21$
$\Rightarrow 6 x = 3 x + 21$
$\Rightarrow 6 x - 3 x = 21$
$\Rightarrow 3 x = 21$
$\Rightarrow x = \frac{21}{3} = 7$
Sarosh's present age is 7 years.
Father's age after 7 years is $6 \times 7 = 42 y e a r s$
His present age is $42 - 7 = 35 y e a r s$
Sum of their present ages $= 35 + 7 = 42 y e a r s$

Question 74.

Krishna and Karan are on the see-saw. Krishna's weight is 60 kg and Karan's is 80 kg. Who among the following kids can help Krishna balance the see-saw. (All of them can sit at extreme ends only).

Peter who has weight of 21 kg
Alison who has weight of 23 kg
Pandu who has weight of 20 kg
Mahi who has weight of 10 kg

Discuss Question

Answer: Option C. -> Pandu who has weight of 20 kg
:
C
It is given that Krishna's weight is 60 kg and Karan's weight is 80 kg. To balance the see-saw Krishna needs another person.
Let the required weight needed to balance the see-saw be

x

kg
Then,

60 + x = 80 x = 80 - 60 = 20

So, Krishna should take help of a kid who weighs exactly 20 kg. Thus, Pandu would be the correct selection.

Question 75.

In a quiz program,the correct answer gets you $2$ marks. For each wrong answer, one mark is deducted from the total score. There are $50$ questions to be answered. If Preeti scored $76$ marks for the quiz, how many of her questions were right?

$26$
$13$
$42$
$38$

Discuss Question

Answer: Option C. ->

42

:
C
As the number of questions answered is unknown, let us assume that unknown variable as '

x

'.
If the number of questions answered correctly are x, then the number of questions answered incorrectly will be

(50 - x)

.
For each correct answer, she gets

2

marks. So the marks scored for x correctly answered questions are

2 x

. Similarly, the marks deducted for (50-x) incorrectly answered questions are

(50 - x) \times 1 = 50 - x

Now, the total marks scored by Preeti will be

2x- (50 -x) = 2x -50 +x = 3x -50

(For each wrong answer, one mark is deducted from the total score)

The final equation is, 3x -50 = 76

3x = 50 +76 = 126

x = \frac{126}{3} = 42

So, the total number of questions answered correctly by Preeti are 42.

Question 76.

If $50$ is subtracted from a number , the result is $4$ . Find the number.

$54$
$46$
$25$
$45$

Discuss Question

Answer: Option A. ->

54

:
A

Let us say 'x' is the number . Given that $50$ is subtracted from it and the result obtained is $4$ .
So mathematically, $x - 50 = 4$ is the equation.
Thus, $x = 50 + 4 = 54$
$54 is the number.$

Question 77.

One pleasant morning, a number 'a' goes for a jog. Another number 'b' passes by 'a' and comments "I am four more than your half”. 'a' gets offended and starts shouting at 'b'. Now, both of them got into a big fight about their value and soon a big crowd gathered. A wise man, Krishna comes, looks at both the numbers, and says, "If you look closely, you are both equals.” 'a' and 'b' realised that the wise man was correct. What are the numbers 'a' and 'b'?

$8, 8$
$8, 4$
$4, 4$
$8, 10$

Discuss Question

Answer: Option A. ->

8, 8

:
A
From the given information,

b = 4 + \frac{a}{2}

The wise man Krishna said that both a and b are equal.

S o, a = b

Hence subsituting in a = b in the first equation , we have

a = 4 + \frac{a}{2}

a - \frac{a}{2} = 4

\frac{a}{2} = 4

a = 8

Since a = b

∴

b = 8

Question 78.

Step 1: $3 x + 2 = 17$
Step 2: $3 x = 17 - 2$
This process of shifting the number from one side of the equation to the other side is called as ___.

translation
root of equation
transposition
correlation

Discuss Question

Answer: Option C. -> transposition
:
C
Transposition is nothing but balancing the other side of the equality when we make any change on one side.
Here, in the equation

3 x + 2 = 17

, when we add

- 2

on both sides, we get

3 x + 2 - 2 = 17 - 2

i.e.,

3 x = 17 - 2

.
Instead of following the above process,

2

is shifted to the other side of the equation.
Therefore, we get

3 x = 17 - 2

This process is known as transposition.

Question 79.

Karan and Kundan are two brothers. Presently Karan's age is four times the age of Kundan. After 6 years Karan's age will be twice as that of Kundan. What is the present age of Kundan?

Discuss Question

Answer: Option C. -> transposition
:

Let the present age of Kundan be $x$ .
So, Karan's present age is $4 x$ .
After 6 years,
Kundan's age = $(x + 6)$
Karan's age = $(4 x + 6)$
Also, Karan's age would be twice of Kundan.
$So, (4x +6) = 2 (x +6)$
$4x +6 = 2x +12$
$x = 3$